The purpose of this model is to understand how genetic architectures of alternative reproductive tactics impact their maintenance in populations. I’m using an individual-based simulation model with different selection scenarios, types of alternative tactics, and genetic architectures (genome-wide additive genetic variance, supergenes, expression networks).

Overview of the model

Males can be courters or not-courters and parents or not-parents. When the model is run with both traits, this results in four possible morphs: courter/parent, courter/not-parent, not-courter/parent, and not-courter/not-parent. Generations are non-overlapping and there is one reproductive bout per generation. In each generation, the population follows the following timeline:

1. Choosing a nest

A female samples 50 males and chooses a male to nest with based on his courtship trait. If there are no courtship traits in the model, she chooses based on the male’s parental trait. If she does not encouter an acceptable male, she does not nest. If she encounters multiple equally-acceptable males, she randomly selects one of them.

2. Fertilization

Once a female decides to nest, up to three males can fertilize the nest. Courters and parental males can contribute more sperm than non-courter and non-parental males: \(r_{courter}=r_{parent}=8\) and \(r_{non-courter}=r_{non-parent}=4\). A courter/non-parent has \(r_{non-parent}\) and a non-courter/parent has \(r_{parent}\). The male with whom the female is nesting gets \(r_{parent}/\Sigma{n_{sperm}}\) and additional non-parental males (up to 2) get \((r_{non-parent}*0.5/\Sigma{n_{sperm}})\), where \(\Sigma{n_{sperm}}\) is the total number of sperm contributed by all of the males, weighted by the sperm competition factor (0.5 is the default for all males except the nesting male). So, when a female mates with one courter and two non-parentals, \(\Sigma{n_{sperm}}\) = \(r_{courter}\) + 2\(*\)(0.5\(*\)\(r_{sneaker}\)), where \(r_{courter}\) = 8 and \(r_{sneaker}\) = 4, therefore \(\Sigma{n_{sperm}}\) = 12.

That being said, every time a male mates he uses his sperm, so after one mating where a courter fertilizes 50% of the female’s 4 eggs, he only has 6 sperm for his next mating.

3. Nest Survival

Before the babies can survive, the nest has to survive. This step is only relevant when parental traits are in the model - if only the courtship trait is specified, then all progeny in the nest survive at this point. When males have the parental trait, if the female has given eggs to a non-parental male (because she chose based on courtship traits), then the nest has a 10% chance of surviving. If the female has given eggs to a parental male, the nest has a 90% chance of surviving.

4. Density-dependent survival

Once the identities of the surviving nests are known–along with the identities of the parents, including sneaker parents–the offspring are created in the simulation. The offspring are created to fill the full carrying capacity of the population, with the numbers per nest being equally divided among all surviving offspring. This allows the population to maintain a constant population size (prior to viability selection) while maintaining the relative successes of the given genotypes/morphs.

5. Viability selection

Before becoming adults, the offspring experience viability selection. Courters and parental males are disfavored in viability selection, with a survival probability of 0.9950125. If an individual is both a courter and a parental male, the survival probability is 0.9900498. Non-courters and non-parental males have survival probabilities of 1.

Evaluating equilibrium

After 10000 generations, I begin tracking the change in frequency of the courter and parent traits, and do so for 2000 additional generations. I calculate the variance in the change in frequency over those 2000 generations. I declare an equilibrium (‘stasis’) has been reached if the last change in frequency of both traits is less than the variance in changes in frequency.

Unlinked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles are all freely recombining and are not adhered to any physical genomic location (aka this is a classical quantitative genetics approach). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Females choose nests based on whether the male is a courter or not, and they all prefer courters all of the time (the female preference does not have a genetic basis and does not evolve). The only way that non-courters produce offspring is through sneaking, but all males can be sneakers (both courters and non-courters). Because parental care is not incorporated in this model, all nests survive.

Frequency of the courter morph (each color represents a different replicate)

Frequency of the courter morph (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters in final generation
CourterFreq CourterW NonCourterW
courter_unlinked_1_summary.txt_1 1 2.13675 0
courter_unlinked_1_summary.txt_2 1 2.03666 0
courter_unlinked_1_summary.txt_3 1 2.06186 0
courter_unlinked_1_summary.txt_4 1 2.03252 0
courter_unlinked_2_summary.txt_1 1 2.13675 0
courter_unlinked_2_summary.txt_2 1 2.03666 0
courter_unlinked_2_summary.txt_3 1 2.06186 0
courter_unlinked_2_summary.txt_4 1 2.03252 0
courter_unlinked_3_summary.txt_1 1 2.13675 0
courter_unlinked_3_summary.txt_2 1 2.03666 0
courter_unlinked_3_summary.txt_3 1 2.06186 0
courter_unlinked_3_summary.txt_4 1 2.03252 0
courter_unlinked_4_summary.txt_1 1 1.95303 0
courter_unlinked_4_summary.txt_2 1 2.04723 0
courter_unlinked_4_summary.txt_3 1 2.02857 0
courter_unlinked_4_summary.txt_4 1 2.07708 0
courter_unlinked_5_summary.txt_1 1 1.95303 0
courter_unlinked_5_summary.txt_2 1 2.04723 0
courter_unlinked_5_summary.txt_3 1 2.02857 0
courter_unlinked_5_summary.txt_4 1 2.07708 0

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph (each color represents a different replicate)

Frequency of parent morph (each color represents a different replicate)

Frequency of parents in final generation
ParentFreq ParentW NonParentW
parent_unlinked_1_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_1_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_1_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_1_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_2_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_2_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_2_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_2_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_3_summary.txt_1 1.2478800 1.57238 1.000000
parent_unlinked_3_summary.txt_2 1.2094800 1.65707 0.586667
parent_unlinked_3_summary.txt_3 1.2352000 1.65618 0.903846
parent_unlinked_3_summary.txt_4 1.2041800 1.67285 0.753846
parent_unlinked_4_summary.txt_1 0.0426554 1.58862 0.779661
parent_unlinked_4_summary.txt_2 0.0423615 1.66887 1.066670
parent_unlinked_4_summary.txt_3 0.0420778 1.76386 1.114750
parent_unlinked_4_summary.txt_4 0.0413643 1.75878 0.666667
parent_unlinked_5_summary.txt_1 0.0426554 1.58862 0.779661
parent_unlinked_5_summary.txt_2 0.0423615 1.66887 1.066670
parent_unlinked_5_summary.txt_3 0.0420778 1.76386 1.114750
parent_unlinked_5_summary.txt_4 0.0413643 1.75878 0.666667

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep

Frequency of the 4 morphs in each rep

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_unlinked_1_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_1_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_2_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_1 11999 Pop0 940 471 469 1000 0.890749 0.443737 0.883452 0.0739653 0.000000 0.362595 -0.942183 -0.832353 1.113290 0.556263 0.362595 0 0 0.556263 0.443737 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_2 11999 Pop1 860 433 427 968 0.890749 0.441109 0.883265 0.0738648 0.000000 0.545455 -0.942183 -0.829546 1.111780 0.558891 0.545455 0 0 0.558891 0.441109 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_3 11999 Pop2 936 473 463 1000 0.890749 0.437632 0.881182 0.0748110 0.000000 0.368421 -0.942183 -0.798195 1.126020 0.562368 0.368421 0 0 0.562368 0.437632 0.000000 NA NA
parent-courter_unlinked_3_summary.txt_4 11999 Pop3 942 477 465 1000 0.890749 0.442348 0.881219 0.0751622 0.000000 0.394737 -0.942183 -0.798750 1.131310 0.557652 0.394737 0 0 0.557652 0.442348 0.000000 NA NA
parent-courter_unlinked_4_summary.txt_1 11999 Pop0 964 465 499 1000 -0.536111 0.565591 -0.587407 0.3684840 1.022810 0.391089 -0.690850 -0.600370 0.649948 0.686022 1.090910 0 0 0.434409 0.313978 0.251613 NA NA
parent-courter_unlinked_4_summary.txt_2 11999 Pop1 962 479 483 1000 -0.536111 0.544885 -0.583240 0.3808790 0.762452 0.435780 -0.690850 -0.607720 0.671811 0.655532 0.936306 0 0 0.455115 0.344468 0.200418 NA NA
parent-courter_unlinked_4_summary.txt_3 11999 Pop2 960 473 487 1000 -0.536111 0.532770 -0.594644 0.3802730 0.777778 0.384615 -0.690850 -0.587605 0.670742 0.670190 0.886435 0 0 0.467230 0.329810 0.202960 NA NA
parent-courter_unlinked_4_summary.txt_4 11999 Pop3 958 479 479 1000 -0.536111 0.582463 -0.564566 0.3733460 0.946237 0.305000 -0.690850 -0.640658 0.658524 0.649269 1.045020 0 0 0.417537 0.350731 0.231733 NA NA
parent-courter_unlinked_5_summary.txt_1 11999 Pop0 964 465 499 1000 -0.536111 0.565591 -0.587407 0.3684840 1.022810 0.391089 -0.690850 -0.600370 0.649948 0.686022 1.090910 0 0 0.434409 0.313978 0.251613 NA NA
parent-courter_unlinked_5_summary.txt_2 11999 Pop1 962 479 483 1000 -0.536111 0.544885 -0.583240 0.3808790 0.762452 0.435780 -0.690850 -0.607720 0.671811 0.655532 0.936306 0 0 0.455115 0.344468 0.200418 NA NA
parent-courter_unlinked_5_summary.txt_3 11999 Pop2 960 473 487 1000 -0.536111 0.532770 -0.594644 0.3802730 0.777778 0.384615 -0.690850 -0.587605 0.670742 0.670190 0.886435 0 0 0.467230 0.329810 0.202960 NA NA
parent-courter_unlinked_5_summary.txt_4 11999 Pop3 958 479 479 1000 -0.536111 0.582463 -0.564566 0.3733460 0.946237 0.305000 -0.690850 -0.640658 0.658524 0.649269 1.045020 0 0 0.417537 0.350731 0.231733 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter. However, 0 of those reps with variation actually crashed.

Linked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles anchored on chromosomes, equally distributed among the chromosomes (4). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

Frequency of the courter morph with linked QTLs (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with linked QTLs in final generation
CourterFreq CourterW NonCourterW
courter_linked_1_summary.txt_1 1 1.99800 0
courter_linked_1_summary.txt_2 1 2.02439 0
courter_linked_1_summary.txt_3 1 1.96457 0
courter_linked_1_summary.txt_4 1 2.02028 0
courter_linked_2_summary.txt_1 1 1.92070 0
courter_linked_2_summary.txt_2 1 2.05350 0
courter_linked_2_summary.txt_3 1 2.00605 0
courter_linked_2_summary.txt_4 1 2.01826 0
courter_linked_3_summary.txt_1 1 1.99800 0
courter_linked_3_summary.txt_2 1 2.02439 0
courter_linked_3_summary.txt_3 1 1.96457 0
courter_linked_3_summary.txt_4 1 2.02028 0
courter_linked_4_summary.txt_1 1 2.00000 0
courter_linked_4_summary.txt_2 1 2.00401 0
courter_linked_4_summary.txt_3 1 2.02020 0
courter_linked_4_summary.txt_4 1 1.94175 0
courter_linked_5_summary.txt_1 1 2.00000 0
courter_linked_5_summary.txt_2 1 2.00401 0
courter_linked_5_summary.txt_3 1 2.02020 0
courter_linked_5_summary.txt_4 1 1.94175 0

Every rep has the courtship trait go to fixation.

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph with linked QTLs (each color represents a different replicate)

Frequency of parent morph with linked QTLs (each color represents a different replicate)

Frequency of parents with linked QTLs in final generation
ParentFreq ParentW NonParentW
parent_linked_1_summary.txt_1 0.600465 1.54780 0.443478
parent_linked_1_summary.txt_2 0.547665 1.64390 0.390805
parent_linked_1_summary.txt_3 0.526249 1.41768 0.302703
parent_linked_1_summary.txt_4 0.574138 1.57957 0.681319
parent_linked_2_summary.txt_1 0.600465 1.54780 0.443478
parent_linked_2_summary.txt_2 0.547665 1.64390 0.390805
parent_linked_2_summary.txt_3 0.526249 1.41768 0.302703
parent_linked_2_summary.txt_4 0.574138 1.57957 0.681319
parent_linked_3_summary.txt_1 0.589370 1.55238 0.424242
parent_linked_3_summary.txt_2 0.580436 1.45682 0.464286
parent_linked_3_summary.txt_3 0.579465 1.68905 0.525773
parent_linked_3_summary.txt_4 0.591772 1.50962 0.752577
parent_linked_4_summary.txt_1 0.240375 1.55125 0.710145
parent_linked_4_summary.txt_2 0.231262 1.73861 0.446429
parent_linked_4_summary.txt_3 0.234927 1.60766 0.734940
parent_linked_4_summary.txt_4 0.236218 1.57267 1.017240
parent_linked_5_summary.txt_1 0.240375 1.55125 0.710145
parent_linked_5_summary.txt_2 0.231262 1.73861 0.446429
parent_linked_5_summary.txt_3 0.234927 1.60766 0.734940
parent_linked_5_summary.txt_4 0.236218 1.57267 1.017240

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

Frequency of the two morphs with linked QTLs (courter = green, parent = blue)

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep with linked QTLs

Frequency of the 4 morphs in each rep with linked QTLs

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation (linked loci)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_linked_1_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_1_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_1_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_1_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_2_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_2_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_2_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_2_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_3_summary.txt_1 11999 Pop0 1000 494 506 1000 -0.458612 0.447368 -0.4942660 0.4957500 0.0090498 0.326007 0.343049 0.376947 0.473095 0.556680 0.330909 0 0.0000000 0.552632 0.443320 0.0040486 NA NA
parent-courter_linked_3_summary.txt_2 11999 Pop1 998 507 491 1000 -0.458612 0.439842 -0.5044700 0.4945260 0.0000000 0.299296 0.343049 0.386529 0.471814 0.560158 0.299296 0 0.0000000 0.560158 0.439842 0.0000000 NA NA
parent-courter_linked_3_summary.txt_3 11999 Pop2 1000 508 492 1000 -0.458612 0.442913 -0.5021480 0.4959020 0.0000000 0.314488 0.343049 0.384785 0.473144 0.557087 0.314488 0 0.0000000 0.557087 0.442913 0.0000000 NA NA
parent-courter_linked_3_summary.txt_4 11999 Pop3 1000 484 516 1000 -0.458612 0.440083 -0.4950940 0.5009730 0.0000000 0.479705 0.343049 0.378210 0.478414 0.559917 0.479705 0 0.0000000 0.559917 0.440083 0.0000000 NA NA
parent-courter_linked_4_summary.txt_1 2042 Pop0 147 69 78 209 0.140770 0.231884 0.1033710 0.0523604 0.0000000 0.509434 -1.438140 -1.214650 0.311778 0.768116 0.509434 0 0.0000000 0.768116 0.231884 0.0000000 NA NA
parent-courter_linked_4_summary.txt_2 2041 Pop1 4 3 1 4 0.140770 0.000000 0.0604539 0.0803165 0.0000000 1.333330 -1.438140 -0.975535 0.462605 1.000000 1.333330 0 0.0000000 1.000000 0.000000 0.0000000 NA NA
parent-courter_linked_4_summary.txt_3 2041 Pop2 151 77 74 194 0.140770 0.363636 0.1098850 0.0542629 0.0000000 0.408163 -1.438140 -1.260750 0.311511 0.636364 0.408163 0 0.0000000 0.636364 0.363636 0.0000000 NA NA
parent-courter_linked_4_summary.txt_4 2041 Pop3 149 76 73 182 0.140770 0.421053 0.1260010 0.0376265 0.1250000 0.568182 -1.438140 -1.345830 0.215691 0.605263 0.630435 0 0.0131579 0.565789 0.381579 0.0394737 NA NA
parent-courter_linked_5_summary.txt_1 2042 Pop0 147 69 78 209 0.140770 0.231884 0.1033710 0.0523604 0.0000000 0.509434 -1.438140 -1.214650 0.311778 0.768116 0.509434 0 0.0000000 0.768116 0.231884 0.0000000 NA NA
parent-courter_linked_5_summary.txt_2 2041 Pop1 4 3 1 4 0.140770 0.000000 0.0604539 0.0803165 0.0000000 1.333330 -1.438140 -0.975535 0.462605 1.000000 1.333330 0 0.0000000 1.000000 0.000000 0.0000000 NA NA
parent-courter_linked_5_summary.txt_3 2041 Pop2 151 77 74 194 0.140770 0.363636 0.1098850 0.0542629 0.0000000 0.408163 -1.438140 -1.260750 0.311511 0.636364 0.408163 0 0.0000000 0.636364 0.363636 0.0000000 NA NA
parent-courter_linked_5_summary.txt_4 2041 Pop3 149 76 73 182 0.140770 0.421053 0.1260010 0.0376265 0.1250000 0.568182 -1.438140 -1.345830 0.215691 0.605263 0.630435 0 0.0131579 0.565789 0.381579 0.0394737 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter. However, 8 of those reps with variation actually crashed.

Supergenes

In these cases, the loci (50) are all located in one region of a chromosome, and that region has reduced recombination. As above, the overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Frequency of the courter morph with supergenes (each color represents a different replicate)

Frequency of the courter morph with supergenes (each color represents a different replicate)

Of the 20 replicates, 0 reached an equilibrium by 10000 generations.

Frequency of courters with supergenes in final generation
CourterFreq CourterW NonCourterW
courter_supergene_1_summary.txt_1 1 1.89394 0
courter_supergene_1_summary.txt_2 1 2.08768 0
courter_supergene_1_summary.txt_3 1 2.03252 0
courter_supergene_1_summary.txt_4 1 2.01613 0
courter_supergene_2_summary.txt_1 1 1.96078 0
courter_supergene_2_summary.txt_2 1 2.00803 0
courter_supergene_2_summary.txt_3 1 2.03666 0
courter_supergene_2_summary.txt_4 1 1.98807 0
courter_supergene_3_summary.txt_1 1 1.89394 0
courter_supergene_3_summary.txt_2 1 2.08768 0
courter_supergene_3_summary.txt_3 1 2.03252 0
courter_supergene_3_summary.txt_4 1 2.01613 0
courter_supergene_4_summary.txt_1 1 2.03265 0
courter_supergene_4_summary.txt_2 1 2.12848 0
courter_supergene_4_summary.txt_3 1 2.04517 0
courter_supergene_4_summary.txt_4 1 2.02240 0
courter_supergene_5_summary.txt_1 1 2.03265 0
courter_supergene_5_summary.txt_2 1 2.12848 0
courter_supergene_5_summary.txt_3 1 2.04517 0
courter_supergene_5_summary.txt_4 1 2.02240 0

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parent morph with supergenes (each color represents a different replicate)

Frequency of parents with supergenes in final generation
ParentFreq ParentW NonParentW
parent_supergene_1_summary.txt_1 1.1443500 1.46189 0.670000
parent_supergene_1_summary.txt_2 1.1917500 1.56757 0.826087
parent_supergene_1_summary.txt_3 1.1563500 1.65963 0.628319
parent_supergene_1_summary.txt_4 1.1744700 1.55932 0.682927
parent_supergene_2_summary.txt_1 1.1443500 1.46189 0.670000
parent_supergene_2_summary.txt_2 1.1917500 1.56757 0.826087
parent_supergene_2_summary.txt_3 1.1563500 1.65963 0.628319
parent_supergene_2_summary.txt_4 1.1744700 1.55932 0.682927
parent_supergene_3_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_3_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_3_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_3_summary.txt_4 0.0404482 1.65455 0.691176
parent_supergene_4_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_4_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_4_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_4_summary.txt_4 0.0404482 1.65455 0.691176
parent_supergene_5_summary.txt_1 0.0415676 1.71264 0.492308
parent_supergene_5_summary.txt_2 0.0403339 1.63820 0.441176
parent_supergene_5_summary.txt_3 0.0401651 1.77017 0.710526
parent_supergene_5_summary.txt_4 0.0404482 1.65455 0.691176

Variation was maintained in 20 of the 20. 0 of the 20 populations crashed, though. Of the 20 replicates, 20 reached an equilibrium by 10000 generations.

Let’s look at the trajectories of the parent traits.

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

The different runs have different outcomes.

Let’s look at the morph frequencies.

Frequency of the 4 morphs in each rep with supergenes

Frequency of the 4 morphs in each rep with supergenes

In some of the runs the population crashed after few generations. This is obvious when looking at the the final frequencies in a table as well:

Frequency of morphs in final generation (supergenes)
Generation Pop PopSize NumMal NumFem NumProgeny ParentThresh ParentAEmean ParentAEsd ParentFreq ParentW NonParentW CourterThresh CourterAEmean CourterAEsd CourterFreq CourterW NonCourterW FreqNcNp FreqCNp FreqNcP FreqCP PrefThresh PrefFreq
parent-courter_supergene_1_summary.txt_1 11999 Pop0 943 472 471 1000 0.890749 0.442797 0.881010 0.0753190 0 0.414449 -0.942183 -0.795600 1.133670 0.557203 0.414449 0 0 0.557203 0.442797 0 NA NA
parent-courter_supergene_1_summary.txt_2 11999 Pop1 944 482 462 1000 0.890749 0.429461 0.881584 0.0739243 0 0.305455 -0.942183 -0.804237 1.112670 0.570539 0.305455 0 0 0.570539 0.429461 0 NA NA
parent-courter_supergene_1_summary.txt_3 11999 Pop2 939 471 468 1000 0.890749 0.456476 0.886884 0.0729530 0 0.312500 -0.942183 -0.884011 1.098050 0.543524 0.312500 0 0 0.543524 0.456476 0 NA NA
parent-courter_supergene_1_summary.txt_4 11999 Pop3 939 479 460 1000 0.890749 0.430063 0.882684 0.0733204 0 0.391941 -0.942183 -0.820793 1.103580 0.569937 0.391941 0 0 0.569937 0.430063 0 NA NA
parent-courter_supergene_2_summary.txt_1 11999 Pop0 943 472 471 1000 0.890749 0.442797 0.881010 0.0753190 0 0.414449 -0.942183 -0.795600 1.133670 0.557203 0.414449 0 0 0.557203 0.442797 0 NA NA
parent-courter_supergene_2_summary.txt_2 11999 Pop1 944 482 462 1000 0.890749 0.429461 0.881584 0.0739243 0 0.305455 -0.942183 -0.804237 1.112670 0.570539 0.305455 0 0 0.570539 0.429461 0 NA NA
parent-courter_supergene_2_summary.txt_3 11999 Pop2 939 471 468 1000 0.890749 0.456476 0.886884 0.0729530 0 0.312500 -0.942183 -0.884011 1.098050 0.543524 0.312500 0 0 0.543524 0.456476 0 NA NA
parent-courter_supergene_2_summary.txt_4 11999 Pop3 939 479 460 1000 0.890749 0.430063 0.882684 0.0733204 0 0.391941 -0.942183 -0.820793 1.103580 0.569937 0.391941 0 0 0.569937 0.430063 0 NA NA
parent-courter_supergene_3_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_3_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_3_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_3_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA
parent-courter_supergene_4_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_4_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_4_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_4_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA
parent-courter_supergene_5_summary.txt_1 11999 Pop0 916 439 477 1000 -0.396641 0.412301 -0.454427 0.5549950 0 0.426357 -0.383509 -0.325517 0.556975 0.587699 0.426357 0 0 0.587699 0.412301 0 NA NA
parent-courter_supergene_5_summary.txt_2 11999 Pop1 959 464 495 1000 -0.396641 0.418103 -0.445153 0.5536360 0 0.362963 -0.383509 -0.334824 0.555611 0.581897 0.362963 0 0 0.581897 0.418103 0 NA NA
parent-courter_supergene_5_summary.txt_3 11999 Pop2 939 454 485 1000 -0.396641 0.411894 -0.442378 0.5484150 0 0.486891 -0.383509 -0.337609 0.550371 0.588106 0.486891 0 0 0.588106 0.411894 0 NA NA
parent-courter_supergene_5_summary.txt_4 11999 Pop3 955 469 486 1000 -0.396641 0.424307 -0.434795 0.5519460 0 0.292593 -0.383509 -0.345219 0.553915 0.575693 0.292593 0 0 0.575693 0.424307 0 NA NA

Multiple morphs are maintained in 0 of the 20 replicates, and those morphs contain either a parent or a courter. However, 0 of those reps with variation actually crashed.